Having cereal for breakfast more often is associated with having more bowls to wash, which is the relationship that most likely reflects correlation but not causation.
What does a correlation means?Correlation means that there is a statistical relationship between two variables, but it doesn't necessarily mean that one variable is causing the other to occur.
In this case, it's possible that people who eat cereal for breakfast simply prefer to use more bowls or have more bowls available to them, rather than the act of eating cereal causing them to use more bowls. Therefore, this relationship reflects correlation but not causation. In contrast, the other two relationships in the options could be argued to reflect causation.
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Jacob's lock combination is a 3 digit number. If the digits cannot repeat, the product of the digits is 84, and the digits are increasing from left to right, how many combinations can Jacob have?
There are a total of 5 + 4 + 2 + 2 + 1 = 14 possible combinations for Jacob's lock.
The first digit of Jacob's lock combination can be any of the factors of 84: 1, 2, 3, 4, 6, 7, or 12.
If the first digit is 1, then the second digit can be any of the factors of 84/1 that are greater than 1 and less than 10 (to avoid repeating digits): 2, 3, 4, 6, or 7. There are 5 choices for the second digit.
If the first digit is 2, then the second digit can be any of the factors of 84/2 that are greater than 2 and less than 10: 3, 4, 6, or 7. There are 4 choices for the second digit.
If the first digit is 3, then the second digit can be any of the factors of 84/3 that are greater than 3 and less than 10: 4 or 6. There are 2 choices for the second digit.
If the first digit is 4, then the second digit can be any of the factors of 84/4 that are greater than 4 and less than 10: 6 or 7. There are 2 choices for the second digit.
If the first digit is 6, then the second digit can only be 7. There is 1 choice for the second digit.
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Use the triangular prisons below to answer questions 6-9. Be sure to show all steps and work.
The prism A have lateral surface area = 685 and total surface area = 1021, while the prism B have lateral surface area = 328 and total surface area = 448.
How to calculate for the lateral and total surface area of the triangular prismsThe triangular prisms A and B have two same size triangle faces and two different size rectangle face with a rectangle bottom face.
For 6 and 7;
area of one triangle face = 1/2 × 21 × 9
area of one triangle face = 94.5
area of the two triangle faces = 2(94.5) = 189
area of one smaller rectangle face = 16 × 14 = 224
area of one bigger rectangle face = 17 × 16 = 272
Area of lateral surface area = 188 + 224 + 272 = 685
Area of bottom rectangle face = 21 × 16 = 336
Total surface area of prism A = 685 + 336 = 1021
For 8 and 9;
area of one triangle face = 1/2 × 24 ×
area of one triangle face = 84
area of the two triangle faces = 2(84) = 168
area of one smaller rectangle face = 7 × 5 = 35
area of one bigger rectangle face = 25 × 5 = 125
Area of lateral surface area = 168 + 35 + 125 = 328
Area of bottom rectangle face = 24 × 5 = 120
Total surface area of prism A = 328 + 120 = 448
Therefore, the prism A have lateral surface area = 685 and total surface area = 1021, while the prism B have lateral surface area = 328 and total surface area = 448.
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you move left 1 unit and move up one unit you end up at 10,0 what did you start with
Answer:
the coordinate is (11,1)
In a board game, the cards you draw tell how many spaces to move. Which expression gives the total number of spaces traveled during the 4 turns?
The expression-4 gives the total number of spaces traveled during the 4 turns can be found using integers or its absolute values.
What are integers?
Integers are the collection of negative, positive numbers including zero. The positive integers lie on the right side of the zero on the number line and the negative lie on the left side of zero on number line. The positive numbers are larger than the negative numbers. Also zero is greater than all negative numbers.The absolute value/modulus of any integer is its magnitude without sign. It is the distance of any given integer from zero.
Here the spaces travelled in each turn is given as +7, +2, +5 and -8.
The total sum of the spaces=(+7) + (+2) + (+5) + (-8)
= 7+2+5-8
=6
The expression in option 1: |7 + -2 + 5 + - 8| which is not equal to 6
The expression in option 2: 7 - 2 + 5 - 8 which is not equal to 6
The expression in option 3: |(+7) + (-2) + (+5) + (- 8)| which is not equal to 6
The expression in option 4: |7 | + |-2| + |5| + |- 8| which is equal to 6
∴The correct expression is option-4
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Fine the surface area of the prism.
The surface area is ? square feet.
By answering the presented question, we may conclude that As a result, surface area the prism's surface area is 640 square feet.
what is surface area ?The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional form is the entire amount of space that surrounds it. The surface area of a three-dimensional form refers to its full surface area. By summing the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you may use the following formula to name the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional form (a three-dimensional shape is a shape that has height, width, and depth).
To get the surface area of the prism, sum the areas of all six faces.
The top and bottom rectangular faces have the same size and area:
10 feet x 8 feet = 80 square feet
The dimensions of the other four faces are the same:
12 feet tall x 10 feet wide = 120 square feet
As a result, the total surface area is:
2 (80 square feet) + 4 (120 square feet) = 160 square feet + 480 square feet = 640 square feet
As a result, the prism's surface area is 640 square feet.
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Find the area of the parallelogram 9m 4m A=b×h =[].9 =[]m2
Answer:
Step-by-step explanation:
The distance from the Earth to the sun is 93 million miles or 93,000,000 miles. How would this number be written in scientific notation?
Answer: To write 93,000,000 in scientific notation, we need to move the decimal point to the left so that there is one non-zero digit to the left of the decimal point.
Counting the number of places we move the decimal point, we get:
93,000,000 = 9.3 x 10^7
Therefore, 93 million miles can be written in scientific notation as 9.3 x 10^7 miles.
Step-by-step explanation:
A 30-foot beam leans against the wall. The beam reaches the wall 16 feet above the ground. What is the measure of the angle formed by the beam and the ground?
(HINT: DRAW THE PICTURE)
The measure of the angle is degrees
(60 points)
the measure of the angle formed by the beam and the ground is approximately 57.76 degrees. the measure of the angle formed by the beam and the ground is approximately [tex]57.76^\circ[/tex] degrees.
What is Right triangles?
A right triangle is a type of triangle that has one angle measuring 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and the other two sides are called the legs.
The Pythagorean theorem is a fundamental concept in mathematics that relates to right triangles, stating that the square of the length of the hypotenuse is equal to the sum of the squares of lengths of two legs.
To solve this problem, we can use trigonometry and the properties of right triangles.
First, let's draw the picture:
In this diagram, we have a right triangle formed by the beam, the wall, and the ground. The height of the triangle is given as 16 feet, and the length of the hypotenuse (the beam) is 30 feet.
We need to find the length of the base of the triangle (the distance between the wall and the bottom of the beam), which we can call d.
Using the Pythagorean theorem, we can find the length of the opposite side of the triangle:
length = √(beam² - wall²)
length = √(30² - 16²)
length = √(900 - 256)
length = √644
length ≈ 25.37 feet
Now we can use the tangent function to find the angle θ:
tan(θ) = opposite/adjacent
tan(θ) = ground/wall
tan(θ) = 25.37/16
tan(θ) ≈ 1.586
To find θ, we need to take the inverse tangent (or arctangent) of 1.586:
[tex]\Theta = tan-1(1.586)[/tex]
[tex]\Theta \approx 57.76^\circ[/tex] degrees
Therefore, the measure of the angle formed by the beam and the ground is approximately [tex]57.76^\circ[/tex] degrees.
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How does f(x)=x change over the interval from x=2 to x=9?
Answer:
The function f(x) = x represents a straight line with a slope of 1, passing through the origin (0,0).
If we consider the interval from x = 2 to x = 9, we can see that the line starts at f(2) = 2 and ends at f(9) = 9.
Therefore, over the interval from x=2 to x=9, the function f(x) = x increases in a straight line fashion from 2 to 9.
In other words, the slope of the line is positive, and the function is monotonically increasing on this interval.
The number of users on a website is 6300 and is growing exponentially at a rate of
73% per year. Write a function to represent the number of users on the website after t
years, where the daily rate of change can be found from a constant in the function.
Round all coefficients in the function to four decimal places. Also, determine the
percentage rate of change per day, to the nearest hundredth of a percent.
The percentage rate of change per day is approximately 0.1932%.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To represent the number of users on the website after t years, we can use the exponential growth formula:
[tex]N_t = N_0 \times e^{rt}[/tex]
where [tex]N_0[/tex] is the initial number of users, r is the growth rate, and t is the time in years.
Given that [tex]N_0[/tex] = 6300 and the growth rate is 73%, or 0.73, per year,
The function is:
[tex]N_t = 6300 \times e^{0.73t}[/tex]
To find the percentage rate of change per day, we can use the formula:
[tex]r = (e^{0.73/365} - 1) \times 100%[/tex]
where 0.73/365 is the daily growth rate.
Solving for r, we get:
[tex]r = (e^{0.73/365} - 1)[/tex] x 100%
r ≈ 0.1932%
Therefore,
The percentage rate of change per day is approximately 0.1932%.
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Pleaee Help apap. THANKS
Answer:
36 sq. inches assuming the shapes are same as well as sides
Find y and x. Pleaseeee helppp
The values are; x = 10 and y = 10.67 according to the figure below.
Define right angle similar triangle?Triangles with the same shape but different sizes are called similar triangles. In comparative triangles, relating points are harmonious and it are corresponding to compare sides.
Apply Pythagoras theorem for the small right angle triangle ΔBCE;
BC² = BE² + EC²
⇒ x² = 8² + 6²
⇒ x² = 64 + 36
⇒ x² = 100
Then, x = 10
Again apply Pythagoras theorem for upper right angle triangle ΔABE;
AB² = BE² + AE²
⇒ AB² = 8² + y²
⇒ AB² = 64 + y²
And also apply Pythagoras theorem for big right angle triangle ΔABC;
AC² = AB² + BC²
⇒ (6 + y)² = AB² + x² (put all above values)
⇒ (6 + y)² = 64 + y² + 10²
⇒ 36 + y² + 12y = 64 + y² + 100
⇒ 12y = 164-36 = 128
⇒ y = 10.67
Therefore, the values are; x = 10 and y = 10.67
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The values are; x = 10 and y = 10.67 according to the given figure.
What is right angle similar triangle?If the hypotenuse and one of the legs of one right triangle are proportional to their relative lengths in the second right triangle, then the two triangles are comparable.
Right triangles don't all look the same. There are two right triangles that we can have where this is not the case. For two triangles to be comparable, the ratios comparing the lengths of their respective sides must all be equal.
Use the Pythagorean theorem to solve the tiny right triangle in ΔBCE;
BC² = BE² + EC²
x² = 8² + 6²
x² = 64 + 36
x² = 100
Then, x = 10
Apply the Pythagorean theorem once more to the triangle with upper right angle ΔABE;
AB² = BE² + AE²
AB² = 8² + y²
AB² = 64 + y²
Apply the Pythagorean theorem to the large right triangle ΔABC as well.
AC² = AB² + BC²
(6 + y)² = AB² + x² (put all above values)
(6 + y)² = 64 + y² + 10²
36 + y² + 12y = 64 + y² + 100
12y = 164-36 = 128
y = 10.67
The values are:
x = 10 and y = 10.67
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Margot gave 12% of x number of dollars that she earned over the summer to an animal rescue shelter.
12% of x is about $60.00. Select all the statements that are true.
Thus, the total earning of Margot during summer is found to be $500.
Explain about the percentage of number:Although the usage of percent and percentage differs slightly, they both signify the same thing. It is customary to use percent or the symbol (%) along with a numerical value.
Although the percentage word was not very ancient, the technique was often used. The Ancient Romans used to calculate fractions as multiples of 1/100 in the absence of the decimal system.
Given :
Let the total earning of Margot be 'x'.Donated amount to animal rescue shelter. = $60Percentage - 12%So,
12% of x = 60.00
x = 60.0 * 100 / 12
x = $500
Total earning amount = $500
Thus, the total earning of Margot during summer is found to be $500.
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Correct question:
Margot gave 12% of x number of dollars that she earned over the summer to an animal rescue shelter.
12% of x is about $60.00. Find the total earning of Margot during summer.
Del Spencer is the owner and founder of Del Spencer's Men's Clothing Store. Del Spencer's has its own house charge accounts and has found from past experience that 10 percent of its sales are for cash. The remaining 90 percent are on credit. An aging schedule for accounts receivable reveals the following pattern:
15 percent of credit sales are paid in the month of sale.
65 percent of credit sales are paid in the first month following the sale.
14 percent of credit sales are paid in the second month following the sale.
6 percent of credit sales are never collected.
Credit sales that have not been paid until the second month following the sale are considered overdue and are subject to a 3 percent late charge.
Del Spencer's has developed the following sales forecast:
May $60,000
June 55,000
July 45,000
August 56,000
September 83,000
Required:
Prepare a schedule of cash receipts for August and September. Round all amounts to the nearest dollar.
A schedule of cash receipts for the months of August and September, all amounts rounded to the nearest dollar has been attached.
Explain what do you mean by accounts receivable?The balance of money owed to a business for goods or services delivered or utilised but not yet paid for by clients is known as accounts receivable (AR). On the balance sheet, accounts receivable are shown as a current asset. Any sum of money that clients owe for purchases they made using credit is known as AR.
The total collection for the months has been provided:
May = $14100
June = $48025
July = $50537
August = $46623
September = $58105
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solve for all solutions of cos(2x)cos(x)-sin(2x)sin(x)=1
The solutions to the original equation are x = 2nπ, where n is an integer.
What is trigonometric identity?A trigonometric identity is an equation that is true for all values of the variables within the domain of the functions involved.
According to question:We can use the trigonometric identity cos(2x) = cos²(x) - sin²(x) to simplify the left-hand side of the equation:
cos(2x)cos(x) - sin(2x)sin(x) = (cos²(x) - sin²(x))cos(x) - 2sin(x)cos(x)sin(x)
Simplifying further using the identity sin(2x) = 2sin(x)cos(x), we get:
(cos²(x) - 3sin²(x)cos(x)) + sin(2x) = 1
Substituting sin(2x) = 2sin(x)cos(x), we get:
cos³(x) - 3sin²(x)cos(x) + 2sin(x)cos(x) - 1 = 0
We can factor this expression as follows:
(cos²(x) - 1)(cos(x) - 2sin(x) + 1) = 0
The first factor has solutions cos(x) = ±1, which means x is an integer multiple of π/2. However, these solutions do not satisfy the original equation, since the left-hand side is always equal to zero.
The second factor gives us the equation cos(x) - 2sin(x) + 1 = 0. We can rewrite this as:
cos(x) + 1 = 2sin(x)
Using the identity sin²(x) + cos²(x) = 1, we can square both sides of this equation to get:
1 + 2cos(x) + cos²(x) = 4sin²(x)
Substituting sin²(x) = 1 - cos²(x), we get:
5cos²(x) - 4cos(x) - 3 = 0
This quadratic equation can be factored as:
(5cos(x) + 3)(cos(x) - 1) = 0
The first factor gives us the solution cos(x) = -3/5, but this is not a valid solution since the cosine function only takes values between -1 and 1.
The second factor gives us the solution cos(x) = 1, which means x is an integer multiple of 2π.
Therefore, the solutions to the original equation are:
x = 2nπ, where n is an integer.
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If f (x) = 3x, g (x) = x + 4, and h (x) = x^2 - 1, find [fo(hog)] (1)
Answer:
Step-by-step explanation:
To find [fo(hog)] (1), we need to first evaluate the composition hog at x = 1, and then plug the result into f.
Let's start by evaluating hog at x = 1:
hog(x) = h(g(x)) = h(x + 4) = (x + 4)^2 - 1
So, hog(1) = (1 + 4)^2 - 1 = 24
Now we can evaluate f at hog(1):
f(hog(1)) = f(24) = 3(24) = 72
Therefore, [fo(hog)] (1) = 72.
The circle graph describes the distribution of preferred transportation methods from a sample of 500 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can be drawn from the circle graph?
Bus is the preferred transportation for 20 residents.
Bicycle is the preferred transportation for 100 residents.
Together, Streetcar and Cable Car are the preferred transportation for 210 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
After analyzing the graph and using the percentages, it can be inferred that Streetcar and Cable Car are the preferred transportation for 168 residents.
What number of residents prefer the transportations mentioned?To draw conclusions from the graph, we can use the percentages to calculate the number of residents who prefer each transportation method.
Number of residents who prefer Walk: 40% of 400 = 0.4 x 400 = 160
Number of residents who prefer Bicycle: 8% of 400 = 0.08 x 400 = 32
Number of residents who prefer Streetcar: 15% of 400 = 0.15 x 400 = 60
Number of residents who prefer Bus: 10% of 400 = 0.1 x 400 = 40
Number of residents who prefer Cable Car: 27% of 400 = 0.27 x 400 = 108
From the given circle graph, we can see that the preferred transportation methods and their percentages are:
Walk: 40%
Bicycle: 8%
Streetcar: 15%
Bus: 10%
Cable Car: 27%
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Solve the right triangle. Round your answers to the nearest tenth.
m∠A = _____ degrees
m∠B = _____ degrees
AB = ____ units
(40 points)
Answer:
m∠A = 50°
m∠B = 40°
AB = 15.5 units
Step-by-step explanation:
This is a right trangle, so we can use the Pythagorean Theorem to calculate AB.
AC² + BC² = AB²
AB² = 11.9² + 10²
AB² = 141.61 + 100
AB = √241.61
AB ≈ 15.5 units
Since this is a right triangle, we only need the angle measurement of either m∠A or m∠B to calculate the angle measurement of the other.
I will use sine function to calculate the angle measurements of A and B. Try to use a more precise value for AB than the rounded answer so our angle measurement will be closer to the actual angle.
sin(m∠B) = 10/15.54381
m∠B = sin⁻¹(10/15.54381)
m∠B = 40.04°
Round to nearest tenth, so m∠B = 40°
m∠A + m∠B + 90° = 180°
m∠A + 130° = 180°
m∠A = 50°
Simplify (4x − 6) − (5x + 1).
Answer:
[tex] - x - 7[/tex]
Step-by-step explanation:
[tex](4x - 6) - (5x + 1)[/tex]
A minus before the parentheses changes the signs in the parentheses to the opposite:
[tex] 4x - 6 - 5x - 1[/tex]
Subtract the number with x's seperately from the plain numbers:
[tex]4x - 5x - 1 - 6[/tex]
[tex] - x - 7[/tex]
Tom and John are engaged in buying and selling certain products A and B. Tom BUYS 5 of product A but
SELLS twice as much of product B. John on the other hand SELLS three times what Tom BOUGHT of
product A and BUYS 13 of product B. At the end of the business day, John banks Ksh 110,000/- while
Tom banks Ksh 230,000.
Under the assumption that the sale prices for product A and B are the same for the two men, and the
costs prices for the products A and B are also the same for the two men, obtain the following:
a) The price for product A and the price for product B (5 marks)
b) If there was a mark up of 25% on the cost price and a discount of 15% on the sale price, how
much would each of the partners have banked at the end of the business day? (10 marks)
Answer:Let's assume that the cost price for both products A and B is "C", and the selling price for both products A and B is "S". We can use this information to set up two equations, one for Tom and one for John, that relate the costs and profits for the two products:
Tom: 5C - 2(5S) = P1
John: 3(5C) - 13C = P2
where P1 and P2 are the profits made by Tom and John, respectively.
We know that at the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh
230,000. So we can write:
P1 = 230,000 - 5C
P2 = 110,000 - 18C
Substituting these values into the equations for Tom and John, we get:
5C - 2(5S) = 230.000 - 5C
Simplifying these equations, we get:
10C - 10S = 230,000
2C = 110,000
Solving for C, we get:
C = 55,000
Substituting this value back into the first equation, we can solve for S:
10(55,000) - 10S = 230,000
Simplifying this equation, we get:
S = 32,000
Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.
Step-by-step explanation:
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8
Which equation could be used to solve for mº?
49⁰
32°
A 49° +32° + m² = 180°
B 49° +32° + m² = 90°
c) 49° +32° = mᵒ
(D) 49 = 32° +m
mº
In the given equation the value of mº is 17°. Answer: (D) 49 = 32° + mº.
What do you mean by the term Triangle and kinds of triangle ?A triangle is a geometrical figure with three straight sides and three angles. It is the simplest polygon and the building block for more complex shapes.
There are several kinds of triangles:
Equilateral triangle: This is a triangle with three equal sides and three equal angles of 60 degrees each.
Isosceles triangle: This is a triangle with two equal sides and two equal angles.
Scalene triangle: This is a triangle with no equal sides or angles.
Right-angled triangle: This is a triangle with one angle of 90 degrees, which is also known as the right angle. The side opposite to the right angle is the longest side, called the hypotenuse, while the other two sides are called legs.
Acute triangle: This is a triangle in which all three angles are acute angles, meaning they are less than 90 degrees.
Obtuse triangle: This is a triangle in which one angle is an obtuse angle, meaning it is greater than 90 degrees. The other two angles are acute angles.
The equation that can be used to solve for mº depends on the given information or conditions. If the problem provides the measures of two angles and their sum, then we can use the equation:
A + B + m = 180°
where A and B are the measures of the given angles, and m is the measure of the unknown angle in degrees.
However, if the problem only gives the measures of two angles and their sum is not required, we can use the equation:
A + B = m
where A and B are the measures of the given angles, and m is the measure of the unknown angle in degrees.
Based on the given information in the question, we are only provided with the measures of two angles, 49° and 32°, and there is no indication that their sum is required. Therefore, the correct equation to solve for mº is:
49° = 32° + mº
We can simplify this equation to solve for mº:
49° - 32° = mº
mº = 17°
Therefore, the value of mº is 17°. Answer: (D) 49 = 32° + mº.
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Can someone help me with these two questions please?
Answer:
Step-by-step explanation:
HELP ASAP PLEASE THIS IS PAST DUE SO YAH HELP AND BRAINLIEST
What is the area of a right triangle with a height of seven and three fourths yards and a base of 20 yards?
140 yds2
155 yds2
thirty eight and three fourths yds2
seventy seven and one half y
Answer: If the height of seven and three fourths yards and a base of 20 yards, then the area of the right triangle is 77.5 square yards.
To calculate the area of a right triangle, we can use the formula:
Area = (base * height) / 2
where the base is one of the sides of the triangle, and the height is the perpendicular distance from that side to the opposite vertex.
In this case, the height of the right triangle is 7 and 3/4 yards, and the base is 20 yards. Plugging these values into the formula, we get:
Area = (20 * 7.75) / 2 = 155 / 2 = 77.5 square yards
In summary, to calculate the area of a right triangle, we can use the formula that relates the base and height to the area. In this case, we needed to use the given values of the height and base of the right triangle to compute the area in square yards.
The resulting area represents the amount of surface inside the triangle and is useful in many applications, such as geometry, physics, and engineering.
Step-by-step explanation:
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Evaluate the function using the Maclaurin series
we use the first four terms, we get: equation.
[tex]f(x) =x^2 + x^3 + x^4/2! + x^5/3![/tex]
And so on.
What is Maclaurin series?A Maclaurin series, named after the Scottish mathematician Colin Maclaurin, is a special type of power series expansion of a function that is centered at zero. In other words, it is a way to represent a function as an infinite sum of terms that involve the function's derivatives evaluated at zero.
The general form of a Maclaurin series for a function f(x) is given by:
[tex]f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...[/tex]
To evaluate the function f(x) = x^2 * [tex]e^x[/tex] using Maclaurin series, we can first find the Maclaurin series for [tex]e^x[/tex] and then multiply it with x^2 to obtain the Maclaurin series for f(x).
The Maclaurin series for [tex]e^x[/tex]is given by:
[tex]e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + ...[/tex]
Multiplying both sides by x^2, we get:
[tex]x^2 * e^x = x^2 + x^3 + x^4/2! + x^5/3! + x^6/4! + ...[/tex]
Therefore, the Maclaurin series for f(x) is:
[tex]f(x) = x^2 * e^x = x^2 + x^3 + x^4/2! + x^5/3! + x^6/4! + ...[/tex]
To approximate the value of f(x) using the Maclaurin series, we can truncate the series after a certain number of terms. The more terms we include, the more accurate the approximation will be. For example, if we use the first three terms of the series, we get:
[tex]f(x) = x^2 + x^3 + x^4/2![/tex]
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Are √2 and √√32 like radicals? Can the sum be simplified?
Answer:
simplifies to 5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]
then
[tex]\sqrt{32}[/tex] = [tex]\sqrt{16(2)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{2[/tex] = 4[tex]\sqrt{2}[/tex]
then
[tex]\sqrt{2}[/tex] + [tex]\sqrt{32}[/tex]
= [tex]\sqrt{2}[/tex] + 4[tex]\sqrt{2}[/tex] ( the 2 terms have like radicals so add coefficients )
= 5[tex]\sqrt{2}[/tex]
Colby went to the bookstore traveling 12 mph and returned home traveling 10 mph. If the total trip took 11 hours, how long did Colby travel at each speed?
____ hours at 12 mph
____ hours at 10 mph
Thus, the time taken by Colby to travel at each speed is-
5 hours at 12 mph and 6 hours at 10 mph.
Define about the relation of speed and time:In the study of physics, the three key variables are speed, distance, and time. How quickly or slowly an object moves through one point to another is determined by the concept of speed. The distance travelled in a unit of time is referred to as speed. Distance is exactly proportional to velocity and speed, while time is constant.
The formula for speed:
speed = distance/time
Then ,
time = distance / speed
Let speed S1 = 12 mph , for this time taken t1.
Let the speed S2 = 10 mph , for this time taken t2.
Since, in each distance is same say 'd'.
Total time t = 11 hours.
t = t1 + t2
t = d/s1 + d/s2
11 = d(1/12 + 1/10)
11 = d(12+10) / (12*10)
d = 11*120 / 22
d = 60 miles.
t1 = 60/12 = 5 hours
t2 = 60/10 = 6 hours.
Thus, the time taken by Colby to travel at each speed is-
5 hours at 12 mph
6 hours at 10 mph
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Circle S is shown where points V, P, and T lie on the circle and tangent lines VK and T'K intersect at point K.
p
S
K
If mVPT = 234° what is the measure of angle LVKT?
In the tangent line , Value of [tex]m\angle{VKT}[/tex] is A)54°.
What is tangent line in the circle?A circle's tangent is a single-pοinted line that intersects the circle. The "pοint οf tangency" is the lοcatiοn where the circle and the tangent crοss. The radius οf the circle, with which it crοsses, is perpendicular tο the tangent. All curved shapes can be thοught οf as tangent. As a tangent is a line, it has an equatiοn as well.
The line that οnly tοuches the circumference οf a circle οnce is said tο be tangent tο it. Fοr each circled pοint, there can οnly be οne tangent. The tangent's pοint οf tangency is where it jοins the circle.
Here the given circle arc length mVPT = 234°. Then
arc length οf mVT = 360°-234° = 126°
Nοw using tangent line fοrmula in circle then,
=> [tex]m\angle{VKT}=\frac{mVPT-mVT}{2}[/tex]
=> [tex]m\angle{VKT} =\frac{234\textdegree-126\textdegree}{2}[/tex]
=> [tex]m\angle{VKT} =\frac{108\textdegree}{2} =54\textdegree[/tex].
Hence the correct option is A)54°.
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Sumi owns a plant store she wants to put 438 plants in 7 equal rows How many plants will be left over after putting them in do
There will be 4 plants left over after putting them in 7 equal rows.
Calculating the number of left over plantsTo find out how many plants will be left over after putting them in 7 equal rows, we need to divide the total number of plants (438) by the number of rows (7) and then find the remainder.
We can use integer division to find out how many plants will be in each row:
438 ÷ 7 = 62
So each row will have 62 plants.
To find out how many plants will be left over, we can subtract the total number of plants from the product of the number of rows and the number of plants in each row:
438 - (7 x 62) = 438 - 434 = 4
Therefore, the number of plants remaining is 4 plants
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The area of a square is 49 mm.
What is the length of each side?
Answer:
Area = 49 mm
Answer:
Step-by-step explanation:
Geometry. Find the value of the variable.
Using intersecting secant theorem, the value of x is approximately 6
How to find the value of the variableThe value of the variable is solved using intersection secant theorem
The theorem gives the formula applied as follows
(6 + 6) * 6 = (5 + x) * x
Starting with the left side of the equation:
(6 + 6) * 6 = 12 * 6 = 72
Now, let's simplify the right side of the equation:
(5 + x) * x = 5x + x^2
Substituting these simplified expressions back into the original equation, we get:
72 = 5x + x^2
This is now a quadratic equation, which we can solve by rearranging and factoring:
x^2 + 5x - 72 = 0
Using calculator the solution is x = 6.35 or -11.35
Taking the positive value we have that x = 6.35
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